Log burners are not usually advised in a rental property and most landlords I speak to are having the taken out. You would need a carbon monoxide alarm in the room with it and would need to follow the manufacturers health and safety advice, (which may include things like regular inspection of the flu etc).
Openrent does not add any wording into their AST around log burners - it is just a standard AST template - so you would need to add custom clauses to cover yourself in this aspect. This is in addition to the safety requirements that David mentioned.
I considered then rejected a log burner in favour of a gas flame effect log burner and I do have a smoke and carbon monoxide alarm fitted but from my own experience of tenants I definitely wouldn’t trust a tenant with an open fireplace or open flame.