Having a cold, the royal baby is upset and peevish (6)
I believe the answer is:
crabby
'peevish' is the definition.
(I've seen this before)
'having a cold the royal baby is upset' is the wordplay.
'having a cold' becomes 'c' (I can't justify this - if you can you should give a lot more credence to this answer).
'the royal' becomes 'r' (abbreviation).
'is upset' indicates anagramming the letters (I've seen 'are upset' mean this).
'baby' anagrammed gives 'abby'.
'c'+'r'+'abby'='CRABBY'
'and' is the link.
Can you help me to learn more?
(Other definitions for crabby that I've seen before include "Sour-tempered like common crustacean" , "petulant" , "Ill-tempered" , "Peevish" , "like one playing with sea? Just so" .)