No need to refelt or "releather" piece as long as the felt/leather itself is okay. Just apply some glue to the base (be careful not to apply too much), let the glue dry thoroughly, it'll never come loose again.
Chess Felt: Should I refelt or glue?
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@chessmaster_diamond Hi, thank you for your reply. May I know what glue specifically should I buy and what brand? The chess pieces are made out of resin, not wood. Should I still buy wood glue?
Most Superglues cover a wide variety of materials, including "resin", metal, wood, letaher etc. Only for wood I use a special glue for wood ("Titebond Wood"), for all other things a regular superglue will do. Just apply carefully and safely.
@chessmaster_diamond Alright! Thank you so much I appreciate it.
There is no need to refelt if the leather is still good.
Just glue. A general purpose glue suitable for leather and resin is OK. There is no need for cyanoacrylate superglue. Clean both surfaces before you glue. Apply only a thin layer of glue. Apply pressure after glueing, e.g. put something heavy on the newly glued pieces.
Okay i'm conflicted since i'm new to taking care of chess sets. I'll wait for more replies in this thread. But thank you for your contribution and comment as well! @tygxc
@desperatekingwalk Hi, thank you for your comment and contribution to this thread. I really appreciate it. 
i honestly hope the leather felt will last for a long time and I don't have to refelt haha. I really like these leather-felted chess pieces.
@desperatekingwalk is it common for people to use superglue when trying to fix the felt? I'm quite worried if I use superglue it would do more harm to the chess piece etc..
Not with the leather bases you have. With felt, you must be careful not to apply too much and let it leak through the porous felt.
just my opinion, 
to answer the question of the thread, glue. normal elmers glue should do
If the felt/leather is peeling loose "ever so slightly" it may be better to peel it off completely, clean and reglue.
@hermanjohnell Hi, thanks for giving your suggestion. Btw since I'm getting conflicting answers, I would like to ask you as well, what glue do you think will be best for leather to resin chess pieces? I would like to get as many answers as possible for leather felt to resin chess pieces.
howthefkdoichess wrote:
@hermanjohnell Hi, thanks for giving your suggestion. Btw since I'm getting conflicting answers, I would like to ask you as well, what glue do you think will be best for leather to resin chess pieces? I would like to get as many answers as possible for leather felt to resin chess pieces.
Since i live in Sweden and we have different glues or the glues have other brands/names it wouldnbe confusing rather than helpful if I told you what I use but if you can find Guterman HT2 i can recommend it.
@hermanjohnell no worries thank you. I searched it up and it is considered a textile glue. Thanks, everyone for your contributions to this post.
howthefkdoichess wrote:
@hermanjohnell no worries thank you. I searched it up and it is considered a textile glue. Thanks, everyone for your contributions to this post.
Yes, it´s a textile glue (which is why it works well with materials such as felt and leather and it bonds well with wood and/or plastic/resin).
Update on the situation: Went to my local Mr.DIY and got myself some UHU Contact "Liquid". It's more like a very sticky thick goo making it hard to navigate while making sure the spread of the glue stays flat. After applying the goo to the felt and chess base, you MUST WAIT 10 minutes for the glue to cure/dry up before letting the felt and chess base touch together. Once the 10 minutes are up, you can start to apply pressure for a few seconds and they will bond together. The results turned out great, although just one piece had a slight bump to the felt as the goo clumped up underneath the chess piece. I had to use my nail to adjust it and spread it out. Overall, not too bad for the first time. I think a thin liquid base would be more of an enjoyable experience. This orangey goo was not too fun hahaha. I went with it since it does say it's great for textile, leather, and all kinds of plastic. Thanks again everyone for your comments.
Hi fellow chess enthusiasts, if the felt on my chess pieces is peeling off ever so slightly, is it okay and a good idea to just apply glue on the felt that is peeling off? This is a leather-like felt, and what kind of glue should I use? The chess pieces are made out of Resin, not wood. Would wood glue still work? The majority of the felt on my chess pieces is fine, just a few that are peeling off and I don't have any extra leather felt/any to begin with. Looking forward to your replies thank you.