Slow progress made by our monarch altering law (5)
I believe the answer is:
crawl
'slow progress' is the definition.
(I've seen this before)
'monarch altering law' is the wordplay.
'monarch' becomes 'CR' (short for Carolus Rex, King Charles in Latin).
'altering' indicates an anagram.
'law' is an anagram of 'awl'.
'cr'+'awl'='CRAWL'
'made by our' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for crawl that I've seen before include "Move as snakes do, or on hands and knees" , "Creep or move slowly" , "swarm" , "Get along swimmingly" , "something used at the pool" .)