Assuming you haven't modified anything which has caused the problem I would think that it's Worn engine mount(s)

This would cause excessive pitching of the engine when putting into gear.

You could observe this with the engine compartment open.

Get an assistant to start the engine and put it in gear

(forward then reverse gears)with the handbrake on.

As they

(slowly) release the clutch see if this shows up the worn component(s).

Similarly at highter revs the engine may become unbalanced if the mounts are worn.
