Showing in the UK will depend on her type!
Can you pop a photo up?
Yes you will have to plait her mane and pull her tail (plaiting tails is just not done in the show ring) regardless of type.
Without pictures, if she is a pure TB I woudl guess at a hack or riding horse type. Which means Ribbon browband with proper rosettes on the ends (I have one for sale BTW).
If she is over 3 years old then she should be shown in her ridden bridle with reins attached to the bit. Bridle should Ideally be very dark brown (havana) and have a flat noseband.
Bit should be either a plain snaffle, pelham or double (always double reins for pelhams and doubles, never roundings).
For inhand classes the handler should ALWAYS wear a tweed jacket with tie and shirt. Inhand trousers and shoes you can run in. (NOT trainers, Jod boots are ideal). BROWN gloves (preferably leather) and a show cane.
Long hair should be put in a bun at the nape of your neck and you should wear a hat (either velvet show hat with flesh coloured harness, beagler or trilby).
Here is a photo of my lad being shown inhand, he is being shown as a hunter hence no pretty browband, but If I were to show him as a riding horse the only thing to change would be the browband!