Turns up in chilly surroundings yet well received (7)
I believe the answer is:
popular
'well received' is the definition.
'popular' can be an answer for 'received' (thesaurus). I'm not certain of the 'well' bit.
'turns up in chilly surroundings' is the wordplay.
'turns' shows that the letters should be reversed in order.
'in' means one lot of letters goes inside another.
'chilly surroundings' becomes 'polar' (I can't explain this - if you can you should give a lot more credence to this answer).
'up' written backwards gives 'pu'.
'pu' put into 'polar' is 'POPULAR'.
'yet' is the link.
Can you help me to learn more?
(Other definitions for popular that I've seen before include "Well liked, generally admired" , "Well-liked" , "appealing to the public" , "Widely admired" , "Non-technical" .)