Hi,
I'd like to know if the part I'm sure is an adverb clause or an adverb phrase - or possibly neither of it.
You can enjoy your holiday now, I'm sure.
A sentence like this is characteristic of relaxed and casual speech and grammar.
I don't see anything adverbial here. Instead, I'd consider these two approaches to understanding what is really meant.
1.You can enjoy your holiday now. I'm sure. ie 2 separate statements
or
2. I'm sure (that) you can enjoy your holiday now. Here, 'I'm sure ' is the main clause and the rest is a subordinate clause explaing what I am sure of.
I favour approach #2. As you can see, it's just rearranging the existing word order.
Best wishes, Clive