Generally liked turning up in the style of a bear (7)
I believe the answer is:
popular
'generally liked' is the definition.
(I've seen this before)
'turning up in the style of a bear' is the wordplay.
'turning' shows that the letters should be reversed in order.
'in the' means one lot of letters goes inside another.
'style of a bear' becomes 'polar' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'up' backwards is 'pu'.
'pu' placed into 'polar' is 'POPULAR'.
Can you help me to learn more?
(Other definitions for popular that I've seen before include "Demotic" , "Trendy" , "Democratic - of general appeal" , "Hot" , "Widely admired" .)