Upright character, married, past the prime. There's no way out of this (7)
I believe the answer is:
impasse
'prime there's no way out of this' is the definition.
The definition suggests a singular noun which matches the answer.
'upright character married past' is the wordplay.
'upright character' becomes 'I' (vertical letter of the alphabet).
'married' becomes 'm'.
'past' becomes 'passe' (I am not sure about this - if you are sure you should believe this answer much more).
'i'+'m'+'passe'='IMPASSE'
'the' acts as a link.
Can you help me to learn more?
(Other definitions for impasse that I've seen before include "deadlock results" , "Stalling of negotiations" , "Standstill" , "hopeless difficulty" , "Situation in which no progress can be made" .)