I am to overtake at the last dead end (7)
I believe the answer is:
impasse
'dead end' is the definition.
(synonyms)
'i am to overtake at the last' is the wordplay.
'i am' becomes 'I'm' (contraction).
'to overtake' becomes 'pass' (as in passing on a road).
'at' means one lot of letters go next to another.
'last' says to take the final letters.
The final letter of 'the' is 'e'.
'im'+'pass'+'e'='IMPASSE'
(Other definitions for impasse that I've seen before include "Stalling of negotiations" , "I permit no further progress" , "Dead end" , "There's no way past it" , "Maybe gridlock" .)