Type of pen with exterior of lime (5)
I believe the answer is:
style
'type' is the definition.
(style can mean a type or variety of something)
'pen with exterior of lime' is the wordplay.
'pen' becomes 'sty' (both can mean an animal enclosure).
'with' is a charade indicator (letters next to each other).
'exterior of' says to hollow out the word (remove centre letters).
'lime' with its middle removed is 'le'.
'sty'+'le'='STYLE'
'of' acts as a link.
(Other definitions for style that I've seen before include "With 1a [OLD], type" , "Cut dash" , "Distinctive arrangement, elegance" , "Phraseology" , "Particular kind, of fashion say" .)