If you mean "to start to have an effect":
* Takes effect
* Begins to work
* Comes into play
* Sets in
* Starts working
If you mean "to enter a place or situation forcefully":
* Barges in
* Busts in
* Charges in
* Storms in
* Forces entry
If you mean "to participate in something actively":
* Gets involved
* Joins in
* Participates
* Takes part
* Chimes in
Please provide more context, and I can give you a more specific synonym. For example, "The medicine finally kicked in," or "He kicked in the door and stormed inside."