Tip: start to search (search methodically) for a kind of cap (9)
I believe the answer is:
cockscomb
'a kind of cap' is the definition.
(I know that cockscomb is a type of cap)
'tip start to search search methodically' is the wordplay.
'tip' becomes 'cock' (I've seen this before).
'start to' indicates taking the first letters.
'search methodically' becomes 'comb' (I've seen this before).
The first letter of 'search' is 's'.
'cock'+'s'+'comb'='COCKSCOMB'
'for' is the link.
(Other definitions for cockscomb that I've seen before include "Rooster's crest" , "Crest on domestic fowl" , "Bird's crest" , "Capital feature of bird" , "one that makes a crow" .)