Recommend last bit of grog's swallowed by drunk guests (7)
I believe the answer is:
suggest
'recommend' is the definition.
(thesaurus)
'last bit of grog's swallowed by drunk guests' is the wordplay.
'last bit of' indicates one should take the final letters.
'swallowed by' means one lot of letters goes inside another.
'drunk' indicates an anagram.
The last letter of 'grog' is 'g'.
'guests' with letters rearranged gives 'sugest'.
'g' going within 'sugest' is 'SUGGEST'.
(Other definitions for suggest that I've seen before include "Insinuate" , "Put forward (an idea)" , "Offer for consideration" , "Intimate" , "Put forward for consideration" .)