The most common and most likely answer to this crossword clue is the 6 letter word SATRAP
I've seen this crossword clue in The Times
S
A
T
R
A
P
More clues leading to the result SATRAP
- Old head has a gin, say, after school
- Bit like regressive old governor
- Governor didn’t stand up to censure
- Old provincial governor finally senses an ambush
- Regions suffering setback with introduction of a tyrant
- Band seizing a governor
- Ruler and predecessor of Sun King, one with power
- Governor took place in parliament, talking rhythmically
- Belt worn by a Persian governor
- Governer wants Gin and It first of all
Buddy explains!

The straight part
We know that "Old head" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old head = satrap.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SATRAP mean?
SATRAP noun- A governor of a Persian province.
- A subordinate ruler.