General:
* Grasping
* Gripping
* Holding tightly
* Clinging
* Clasping
* Seizing
More specific:
* Expressing fear or anxiety: Squeezing, clutching, gripping
* Holding something dear: Cherishing, embracing, treasuring
* Trying to control: Grasping, seizing, gripping
* Holding onto something for support: Leaning on, clinging to, relying on
Figurative:
* Holding onto an idea or belief: Adhering to, clinging to, embracing
* Holding onto a hope: Cherishing, clinging to, grasping at
The best synonym will depend on the specific meaning you want to convey.