Hyrule:

Only in TP Zelda appears to be in power.
Patriarcal
Gerudo

There's an old lady in charge during FSA but I can't find a picture of her.
Patriarcal
Goron
...they have no females.
Patriarcal
Zora-Lanayru

Not in charge in TP because he had died. Succeeded by Prince Ralis after his motehr died.
Patriarcal
Kokiri
I'm fairly certain the Great Deku Tree is male. Call it a hunch based on the moustache.
Patriarcal
Gohma
These have Queens, no argument here.
Matriarcal
Ordona

Patriarcal
Deku

Patriarcal
Moblin
If the Moblins have females I don't want to know it

Patriarcal
Darknut
Never saw any voluptous breastplates on these fellows.
Patriarcal
Lizalfos
In the official games they are not gender specified, but I don't mind them being matriarcal, makes sense for lizards. Still in canon it's...
Undefined
Stalfos
They lack genitals.
Undefined
Sheikah
We've only seen a handful and never one elevated above the others.
Undefined
Labrynna
They did have a queen. No doubt about this one.
Matriarcal
Fairies
Of course fairies are predominately females (we've seen like one male in the whole series).
Matriarcal
Ikana

Even without a crotch this was clearly a dude.
Patriarcal
Twili
Ruled by a princess... I could argue that if she hadn't taken the title queen that'd mean she'd pass her powers to her husband upon marrying, but I'll concede this one.
Matriarcal
Wizzrobe
Who even knows.
Undefined
River Zora

That is a dude. Though Ruto was originally going to be a River Zora princess, odds are she would have had a father in charge.
Patriarcal
Oocca
I don't even wanna know about this one.
Undefined
Majora
Ironically, though Neph has given it male laughter Majora might actually be female. In the end, I'll say...
Undefined
Horon

Patriarcal
Zuna
No way to know.
Undefined
Subrosian
Same as above.
Undefined
Tokay
And yet again.
Undefined