Obsequious and silly chap isn't coy (11)
I believe the answer is:
sycophantic
'obsequious' is the definition.
('sycophantic' can be a synonym of 'obsequious')
'silly chap isn't coy' is the wordplay.
'silly' indicates an anagram.
'chap'+'isnt'+'coy'='chapisntcoy'
'chapisntcoy' anagrammed gives 'SYCOPHANTIC'.
'and' acts as a link.
(Other definitions for sycophantic that I've seen before include "Flattering" , "Servile, toadying" , "Unctuous" , "tending to fawn" , "Crawling" .)