Limited number concealing onset of such longing (6)
I believe the answer is:
thirst
'such longing' is the definition.
'thirst' can be an answer for 'longing' (thirst can mean a longing or desire). I am not certain of the 'such' bit.
'limited number concealing onset' is the wordplay.
'limited' says to take the centre (the limits of the word are removed).
'number' becomes 'anaesthetist' (someone who numbs people before surgery).
'concealing onset' becomes 'irst' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The centre of 'anaesthetist' is 'th'.
'th'+'irst'='THIRST'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for thirst that I've seen before include "Quaff to slake it" , "Drink to slake it" , "Physiological need to drink" , "A need (for liquid)" , "lack of water" .)