You Do Need power plug adapter while traveling from Turkmenistan to Gibraltar.

Here is Why You Need An Adapter

The outlet and plug type used in Gibraltar is G and in Turkmenistan are C and F. This is how they look like.

Turkmenistan

In Turkmenistan, outlets of type C and F are in use.

Type C

Type F

Gibraltar

In Gibraltar, outlets of type G are in use.

Type G