Pest that is seen outside becomes angry (5)
I believe the answer is:
irate
'angry' is the definition.
(irate can mean angry or annoyed)
'pest that is seen outside' is the wordplay.
'pest' becomes 'rat' (rat can mean a nasty person).
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'seen outside' indicates putting letters inside.
'rat' placed within 'ie' is 'IRATE'.
'becomes' acts as a link.
(Other definitions for irate that I've seen before include "Spitting feathers" , "Not happy" , "Boiling" , "Aggrieved" , "will be up in arms" .)