Deity with short name, an old character (5)
I believe the answer is:
thorn
'an old character' is the definition.
(letter used in Old English)
'deity with short name' is the wordplay.
'deity' becomes 'thor' (Thor is an example**).
'with' means one lot of letters go next to another.
'short' indicates taking the first letters.
The first letter of 'name' is 'n'.
'thor'+'n'='THORN'
(Other definitions for thorn that I've seen before include "Sharp point; runic character" , "Sharp point on, eg, rose" , "Prickly plant" , "Plant spine; old letter" , "Invariable accompaniment of 2, they say" .)