A letter gets mailed out? That's wise (7)
I believe the answer is:
sapient
'wise' is the definition.
('sapient' can be similar in meaning to 'wise')
'a letter gets mailed out?' is the wordplay.
'letter' becomes 'pi' (pi is a kind of letter**).
'gets' means one lot of letters go next to another.
'mailed' becomes 'sent' ('send' can be a synonym of 'mail').
'out?' means one lot of letters goes inside another.
'a'+'pi'='api'
'api' going inside 'sent' is 'SAPIENT'.
'that's' is the link.
(Other definitions for sapient that I've seen before include "Acutely insightful and wise" , "very keen" , "Discerning" , "Literary word for wise" , "Canny" .)