Providing food for pet close to Alice with a strange grin (8)
I believe the answer is:
catering
'providing food' is the definition.
'pet close to alice with a strange grin' is the wordplay.
'pet' becomes 'cat' (I have seen 'Common pet ' mean 'cat' so perhaps 'pet' could also mean 'cat'**).
'close to' indicates one should take the final letters (the close/ending of).
'with' says to put letters next to each other.
'a strange' indicates an anagram.
The last letter of 'alice' is 'e'.
'grin' with letters rearranged gives 'ring'.
'cat'+'e'+'ring'='CATERING'
'for' acts as a link.
(Other definitions for catering that I've seen before include "Providing food, entertainment etc." , "essential feature of the tourist industry" , "Providing food and drink" , "activity at event" , "Making allowances" .)