1.
If someone closes up a building, they shut it completely and securely, often because they are going away.
Just close up the shop...
The summer house had been closed up all year.
= shut up, lock up
PHRASAL VERB : V P n (not pron) , V-ed P
2.
If an opening, gap, or something hollow closes up , or if you close it up , it becomes closed or covered.
Don’t use cold water as it shocks the blood vessels into closing up.
PHRASAL VERB : V P , also V n P