The first of the strays should be searched for (6)
I believe the answer is:
sought
'searched for' is the definition.
(I've seen this before)
'the first of the strays should' is the wordplay.
'the first of' says to take the initial letters.
'should' becomes 'ought' (synonyms).
The first letter of 'strays' is 's'.
's'+'ought'='SOUGHT'
'be' is the link.
(Other definitions for sought that I've seen before include "Looked for" , "Wanted" , "Tried to find" , "Attempted to find" , "Searched for - investigated - desired" .)