Chair with support to pick up capsized fishers so (13)
I believe the answer is:
professorship
'chair' is the definition.
('professorship' can be a synonym of 'chair')
'support to pick up capsized fishers so' is the wordplay.
'support' becomes 'prop' (prop is a kind of support**).
'to pick up' indicates putting letters inside.
'capsized' indicates anagramming the letters.
'fishers'+'so'='fishersso'
'fishersso' is an anagram of 'fessorshi'.
'prop' going around 'fessorshi' is 'PROFESSORSHIP'.
'with' acts as a link.
(Other definitions for professorship that I've seen before include "University post" , "Academic position" , "Academic post" , "University chair" .)