[12] Connolly made his debut on 14 August, starting in a League Cup match as a right-back against Championship side Millwall which ended 2–2, with Crawley winning 4–1 on penalties.
[14] In late August 2012, Connolly was part of the Crawley team which successfully defeated Bolton in the League Cup thanks to a last minute goal by Nicky Ajose.
[17] In a home match against Brentford on 26 February 2013, Connolly gave away a penalty and received a red card after 50 seconds, with Crawley going on to lose 2–1.
[28] On 22 February 2015, Connolly was injured during Kilmarnock's 3–3 draw against Inverness Caledonian Thistle[29] and it was later confirmed he had broken his collarbone with the injury expected to keep him out for the remainder of the season.
[31] Ahead of the 2015–16 season Connolly was named as captain of Kilmarnock, replacing Manuel Pascali who had left the club earlier in the summer.
[38] He was part of the United team that were 14 points clear at the top of the Championship table when the 2019–20 season was curtailed due to the COVID-19 pandemic; they were subsequently declared champions and promoted to the Premiership.
[40] The following month, he was charged with "not acting in the best interests of football" and breaching COVID regulations, when he allegedly refused to wear a face mask in a taxi.
[45] On 17 January 2022, Connolly returned to his home country, signing for League of Ireland Premier Division club Dundalk on a six-month loan deal.
[48] After ending his loan spell at Dundalk, Dundee United sold Connolly to Derry City on 28 July 2022 for an undisclosed fee.