Tighten up, seeing nurse welcome spat (7)
I believe the answer is:
stiffen
'tighten up' is the definition.
('stiffen' can be a synonym of 'tighten up')
'nurse welcome spat' is the wordplay.
'nurse' becomes 'sen' (I've seen this before).
'welcome' is an insertion indicator (in sense of 'inviting in').
'spat' becomes 'tiff' ('tiff' can be a synonym of 'spat').
'sen' enclosing 'tiff' is 'STIFFEN'.
'seeing' is the link.
(Other definitions for stiffen that I've seen before include "Make rigid or inflexible" , "Make hard" , "more severe" , "Make unbending" , "Reinforce" .)