Princess has second thoughts - and goes down (4)
I believe the answer is:
dips
'goes down' is the definition.
(dipping is a kind of going down)
'princess has second thoughts' is the wordplay.
'princess' becomes 'di' (Princess Diana).
'has' means one lot of letters go next to another.
'second thoughts' becomes 'ps' (as in a PS in a letter).
'di'+'ps'='DIPS'
'and' is the link.
(Other definitions for dips that I've seen before include "Lowers into liquid" , "Briefly immerses" .)