As letters may be, initially encouraging headlong rush (8)
I believe the answer is:
stampede
'headlong rush' is the definition.
(I've seen this in another clue)
'as letters may be initially encouraging' is the wordplay.
'as letters may be' becomes 'stamped' (as in stamps on letters in the post).
'initially' indicates taking the first letters.
The first letter of 'encouraging' is 'e'.
'stamped'+'e'='STAMPEDE'
(Other definitions for stampede that I've seen before include "Pasted me (anag.)" , "Uncontrolled rush" , "Wild run of frightened cattle" , "Sudden rush of a panicstricken herd" , "herd scatter wildly" .)