The first dray, terribly late (5)
I believe the answer is:
tardy
'late' is the definition.
(I know that late can be written as tardy)
'the first dray terribly' is the wordplay.
'the first' becomes 't' (1st letter of 'the').
'terribly' indicates an anagram.
'dray' with letters rearranged gives 'ardy'.
't'+'ardy'='TARDY'
(Other definitions for tardy that I've seen before include "Late, delayed" , "Backward" , "Late - slow" , "Behindhand" , "Unpunctual" .)