[4] Aged 20 Williams was signed by Scarlets, being developed for his first year in 2010–11 at Llanelli RFC, making his debut against Carmarthen Quins in March 2010.

Williams then went on to make his Scarlets regional debut against Connacht on 10 September 2011 and scoring his first try in the away defeat to Benetton Treviso on 1 October 2011.

This included crossing for the opening try in the final against Munster, with Scarlets eventually running out as 46–22 winners at the Aviva Stadium.

In 2017, it was announced that Williams would join Premiership Rugby side Saracens in England on a three-year contract from the 2017–18 season.

[12] In November 2024, Williams announced he would be leaving the Kubota Spears in favour of a move back to the UK for family reasons.

[14] Williams made a try-scoring second debut for the club in a Champions Cup win against Stade Français in December 2024.

[17] Williams was called up to the Wales squad for the 2015 Rugby World Cup, despite being a doubt following surgery on his foot in June 2015.

Wood managed to avoid a ban for the kick, with citing commissioner Maurizio Vancini preferring to give a warning.

[24] After impressing in the 29–25 win against Australia, Williams scored again in the following game against Fiji, helping Wales to secure their qualification for the quarter-finals.

After overcoming France and booking their place in the semi-finals, Williams suffered an ankle injury ahead of the game, ruling him out of the rest of the tournament.

[28] Williams was selected for his second British and Irish Lions tour in May 2021 against the World Cup holders South Africa.