Use tenacious to mean "not easily letting go or giving up," like a clingy child who has a tenacious grip on his mother's hand.
A strong grip or an unyielding advocate might both be described as tenacious, a word whose synonyms include resolute, firm, and persistent. The word comes from the Latin root tenax, which means "holding fast." The basketball commentator Marv Albert, impressed by a defender's skill, once uttered the sound bite, "That's some tenacious D!" ("D" is short for "defense.") The musicians Jack Black and Kyle Gass borrowed the phrase for the name of their comedy-rock band, Tenacious D.