To start with, journey each time leaves a group with a sleep problem (3,3)
I believe the answer is:
jet lag
'a sleep problem' is the definition.
The definition suggests a singular noun which matches the answer.
'to start with journey each time leaves a group' is the wordplay.
'to start with' indicates taking the first letters.
'group' becomes 'g' (this might be a standard abbreviation I've not previously seen).
The first letters of 'journey each time leaves' is 'jetl'.
'jetl'+'a'+'g'='JET-LAG'
'with' acts as a link.
Can you help me to learn more?
(Other definitions for jet lag that I've seen before include "Exhaustion after air travel" , "Effect of long-distance flight" , "It sometimes results from international travel" , "Discomfort due to changing time zones when flying" , "Bad effect of air travel" .)