As MacBook Pros recently celebrated their 13th birthday and there are easily over 100 variants, what you can do depends on the MacBook Pro sub-model and the kind of drive it has. Some have easily-accessed standard rotational drives, some have solid-state drives that may require a special enclosure after removal, and the most recent MBPs do not have removable storage at all.
As the computer obviously doesn't start, you can use the serial number--stamped in a tiny font on the bottom cover--to find your sub-model from this Apple support link:
Check Your Service and Support Coverage - Apple Support
Sub-models include a year and possible the modifiers "Early, Middle, Late" plus the screen size, and if it is a Retina display model. If you tell us that we can be much more specific in helping you.
A new MBP will not have have a place for a traditional drive so you will have to get an simply external enclosure or bare drive adapter to transfer the files.