Bridge partner, the so-called "fourth" (5)
I believe the answer is:
forth
'bridge partner the' is the definition.
I can't judge whether this definition defines the answer.
'so-called fourth' is the wordplay.
'so-called' indicates a 'sounds like' (homophone) clue.
'fourth' sounds like 'FORTH'.
Can you help me to learn more?
(Other definitions for forth that I've seen before include "(Go) away" , "River and estuary in eastern Scotland" , "Scottish river and firth" , "Onward direction" , "Water" .)