Instinctively let in any strays (8)
I believe the answer is:
innately
'instinctively' is the definition.
(I've seen this before)
'let in any strays' is the wordplay.
'strays' indicates an anagram.
'let'+'in'+'any'='letinany'
'letinany' is an anagram of 'INNATELY'.
(Other definitions for innately that I've seen before include "Inherently, instinctively" , "Naturally, inherently" , "from birth" , "How kids react" .)