Modern Vespa

Has anyone connected heat great to their Vespa GTS300 such as jacket and gloves?

I meant to say heated gear.

Just do a site search lots of threads on it

I use a heated jacket and heated grips on my GTS250. no problem

You can connect heated gear to your Vespa. I personally have heated grips.
If you wanted to connect heated jackets and gloves, then you would want a charging port that is mounted in a place you can connect to while riding.
Just have to make sure that all the things that you connect to the charging port has a total load less than what the circuit can handle.
Also make sure the way you connect the charging port that it is only on when you start the vehicle.
It is easy to accomplish and there are plenty of solutions, you can find one that you like to adapt for your needs.
Summer is good time to get all these things done before the cold weather comes.

This is a bit like asking directions in a gas station and being told to use a map.

Generally speaking, people who ask questions on a forum are usually looking for answers that aren't immediately obvious via search. Either they don't know the right search terms, or they are overwhelmed with results that may or may not be relevant.

Rather than tell someone to do a search, it's usually far more productive to point them in the right direction.