Horse carrying Frenchman in search (4)
I believe the answer is:
comb
'search' is the definition.
(combing is a kind of searching)
'horse carrying frenchman' is the wordplay.
'horse' becomes 'cob' (cob is a kind of horse).
'carrying' indicates putting letters inside.
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'cob' enclosing 'm' is 'COMB'.
'in' acts as a link.
(Other definitions for comb that I've seen before include "Implement with teeth" , "Toothed device - crest" , "Hair-tidier" , "Rummage through" , "Toothed instrument" .)