Very short of time and long to get to end of July (6)
I believe the answer is:
'very short' is the definition.
(I've seen this before)
'time and long to get to end of july' is the wordplay.
'time' becomes 't' (abbreviation).
'and' says to put letters next to each other.
'long' becomes 'itch' (to long or itch for something is to desire it).
'to get' says to put letters next to each other.
'to end of' indicates one should take the final letters.
The final letter of 'july' is 'y'.
'of' acts as a link.
(Other definitions for titchy that I've seen before include "Tiny" , "Very small" , "Very short" , "Little" .)