As a "Royal" regiment, the facings, cuffs, and breeches would have been blue. The coat and waistcoat, would have been red. All edging to cuffs and lapels, and to buttonholes, would be in an intricate woven lace. The Funckens give this as being half white, with diagonal red stripes, a quarter blue, and the outer quarter yellow. As in all regiments, the front of the mitre cap would have been in the facing colour, blue. As the 23rd had a distinctive badge, the three white feathers of the English prince of Wales, this would have been embroidered on the front. The lower flap at the front was, as in all regiments, red with the white horse of Hannover, edged with the motto "Nec Aspera Terrent". The rear of the mitre would have been red, piped with white.
The King's colour was the Union flag of the period, with in the centre the feathers in a crowned wreath of foliage, pink roses, thistles and shamrock. The regimental colour would have been blue with the union in the canton, and the same feathers and wreath in the centre. In the other three corners was an oval cartouche. Offhand, I can't remember which was where, bit I believe one was the red dragon rampant, and another depicted the sun rising over the mountains. I'll see if I can find more accurate details.
Ed