broad, wide | narrow | tight | loose | adjustable, detachable
The bag comes with detachable straps.

elastic, elasticated, padded | carrying, safety
a portable radio with a carrying strap

ankle, chest, shoulder, waist, wrist, etc. | bra, watch, etc.

buckle (up), do up, fasten | unbuckle, undo, unfasten | tighten | loosen | adjust | attach, clip on, fit
He clipped on his safety strap. | The camera was fitted with a strap.

on a/the ~
His binoculars were on a strap round his neck.

~ across, ~ around/round, etc.
She had a wide leather strap around her wrist.

safely | firmly, tightly | down, in, on
He strapped his gun belt on.

into
Make sure that the child is strapped tightly into the buggy.

to