Thomas was the son of William Brunce (alias Brouns), the Lord of the Manor of Sutton Courtenay in Berkshire. He grew up at the Manor House, then called 'Brunce's Court' and, by 1404, was sent to Oxford to obtain his education. This was possibly at New College, which was certainly attended by his friend, Thomas Beckington, who was to become the Rector of Sutton Courtney Church and eventually Bishop of Bath and Wells. 

He was very early made Rector of Appleton Church, not far from his home in Berkshire. Later appointments were to rectories further into the Midlands, but he may have been largely an absentee clergyman as his studies in Oxford continued. By 1412, however, he obtained the living of St. Aldate's in that city and, around the same time, became a legal advisor to Oseney Abbey. Two years later, he was elected sub-dean of Lincoln Cathedral and he seems to have moved north once more. Appointments as a canon of Lincoln, prebendary of Welton Westhall, portioner of Hibaldstow, prependary of St. Botolph's (Lincoln) and prebendary of Langford Manor, all in that same county, followed over the next decade.

In 1419, Thomas vacated the sub-deanship and took the position of Archdeacon of Stow. It was in the April of the following year that he first became embroiled in National politics. He was charged to act as envoy for King Henry V in France, arranging an interview for him with the King of France and the Duke of Burgundy. Then, in July, he was sent on a mission to treat with the Bishop of Nantes and others concerning the release of Arthur of Brittany. 

Such missions across the Channel required a residence near the south coast and, despite his positions in the East Midlands, Thomas settled in Kent, taking on appointments as warden of the altar of Goldes in All Saints' Church, Maidstone and Vicar-General in Spirituals to the Bishop of Rochester. Added to these were the more prestigious positions as a member of the council of the Prior of Christ Church Cathedral in Canterbury and Chancellor to the Archbishop himself.

With Dr. William Lyndwood, he was appointed, in 1425, to carry out a metropolitical visitation in his old stamping ground, at Merton College, Oxford. He was also an auditor of causes at the Court of Canterbury. Two years later, he managed to secure the Archdeaconry of Berkshire, no doubt allowing him visits home at no personal expense. 1429 saw him becoming a canon and prebendary of Chichester, a step on the road to his election as Bishop soon afterward. Letters commendatory, on his behalf, were addressed by Oxford University to the Pope but, though the Royal assent was signified, the provision was not granted and Simon Sydenham took up the position instead. 

Thomas' hopes of a bishopric were raised again in 1435. The Papacy provided for him to become Bishop of Worcester, but the appointment was rescinded in deference to the King's wish for the promotion of Thomas Bourchier to that see. Luckily, he was offered Rochester instead and was consecrated at Canterbury on 1st May 1435. Thomas was there barely a year, when he was transferred to the richer see of Norwich. Unfortunately, however, he had to tender his apologies to Henry V for his receipt of the bull of translation without Royal consent having been previously obtained, while he was attending the Council of Basel. The new Bishop was soon back in the Royal good books though and received a number of embassies: negotiating a peace with France and a commercial treaty with Flanders, both in 1439.

In ecclesiastical matters, Bishop Brunce was obliged to settle a major dispute between the Prior and Convent of his Cathedral Church and the citizens of Norwich; and, despite having to obtain redress at the Roman Curia for an affront to his episcopal dignity from his Prior, he was remembered fondly by the Cathedral for upholding their rights, as well as erecting the great rood loft there.