The Breviate Chronicle for the year 1041 notes:

'bellum pencadeir in quo grifinus superauit hoelum' (Gough-Cooper, b1062.1).
Translation: 'The battle of Pencadair in which Gruffydd overcame Hywel' (Remfry, 173).

This was a battle between Gruffydd ap Llewelyn, king of Gwynedd and Hywel ab Edwin the king of Deheubarth. The location is confirmed by Gerald of Wales who, writing in 1191, states that, `Not far to the north of Carmarthen lies Pencader? (Thorpe, 139). There seems no reason to dispute a location here (SN 445 360) (Charles-Edwards, 562).

RCAHMW (Battlefields Inventory), Dec 2016

Bibliography
Charles-Edwards, T. M., Wales and the Britons 350?1064 (Oxford University Press, 2013).
Gough-Cooper, Henry (ed.) The Breviate Chronicle: Annales Cambriae, The B Text from London, National Archives, MS E164/1, pp. 2?26, online edition.
Remfry, Paul M. Annales Cambriae: A Translation of Harleian 3859: PRO E. 164/1: Cottonian Domitian, A1: Exeter Cathedral Library MS.3514 and MS Exchequer DB Neath, PRO E. 164/1 (Castle Studies Research, 2007).
Thorpe, Lewis (trans.), Gerald of Wales The Journey through Wales and The Description of Wales (Penguin, Harmondsworth, 1978).