Head to the village of Marignac, then take Rue du Burat, which runs alongside the stream of the same name. Continue along the forest road and then the track heading south. Park in the car park at the Marignac picnic area.
(S/E) Head due south along the path running parallel to the Ruisseau de Burat to reach the Cabane Contraire.
(1) Continue southwards, first along a path then along a wider track. At a hairpin bend, you’ll come across another track. Leave these tracks and head straight ahead along a path to reach the Cabane de Saribarolle.
(2) After the small bridge, turn right and avoid the poor shortcuts. Follow the yellow markings. Please note that from here, a few sections on a fairly steep slope make this route more difficult. Continue the ascent to reach the Burat Clearing junction at the edge of the forest.
(3) Turn left and go round Lake Burat. Pass to the south of the lake and continue diagonally off-track through the bushes to reach a more clearly marked path. Take this to the left to reach the Col de Saint-Béat.
(4) Turn right almost 180° to climb up the ridge on the right, initially following the wire fence and then staying firmly on the ridge. Please note that this climb is very steep; finish the climb at the summit of Pic de Burat.
(5) Begin the descent by following the ridge opposite towards the west on the green-marked path. Then head for the Port de Burat junction.
(6) Turn right to quickly reach the Cabane de Burat, recognisable by its green roof.
(7) Continue the descent straight ahead and return to the crossroads at the clearing you passed on the way up.
(3) Follow the route you took on the way there in the opposite direction to return to the car park at the Marignac picnic area (S/E)..
I do not recommend doing the circular in the other direction, as this would mean descending the St Beat - Burat pass, which is very steep and would not be pleasant. I didn't see any ibex, but there were lots of birds of prey at the summit, including griffon vultures, bearded vultures and golden eagles: for me, this is the highlight of the hike. As mentioned in another comment, this hike is not suitable for children or beginners.