Hegarty's senior career began as a striker with Hamilton Accies in 1972. In November 1974, Dundee United manager Jim McLean signed him for a fee of £27,500. Two years later, McLean transformed Hegarty's career when he experimented by pairing him with Dave Narey in United's central defence. The partnership they forged would be integral to United's successes for over a decade, and Hegarty, would develop into a top class central defender. As club captain, Hegarty led United to their first ever major trophy, the Scottish League Cup in 1979, which they retained the following year.
In 1982–83, Hegarty was an ever-present as United captured the Scottish League title. He also featured in many notable victories in European competition, albeit injury restricted his participation in United's run to the 1987 UEFA Cup Final.
Hegarty represented his country between 1979 and 1983, captaining the side against Northern Ireland in his eighth and final appearance for Scotland. He is widely regarded as one of the best central halves to have never been a regular for Scotland. He also turned out for the under-21 side as a permitted over-age player and represented the Scottish League.
In recognition of his contribution to Dundee United, the club allowed him to leave on a free transfer in January 1990. He briefly played for St. Johnstone, helping them to promotion, before joining Forfar Athletic as player/manager. His tenure at Station Park ended in relegation in 1992 and Hegarty left shortly afterwards. Hegarty's next role was a return to Dundee United when he was offered a position on the club's coaching staff. After leaving Tannadice again in 1995 he went on to work for Hearts and Aberdeen in coaching capacities, returning to management at Aberdeen. Following the dismissal of Alex Miller, he was appointed as manager on an interim basis in January 1999. However, despite saving the club from relegation, Aberdeen elected at the end of the season not to continue with Hegarty in the job on a long-term basis. Once again, Dundee United offered Hegarty a coaching role, which became a manager role in October 2002 after chairman Eddie Thompson was unable to prise first-choice Ian McCall from Falkirk. Initially appointed as caretaker, Hegarty's role was to be extended until the end of the season before he was sacked in January 2003 – and subsequently replaced with McCall.
Since his latest departure from Tannadice, Hegarty continued to work in coaching, having been on the staff of both Livingston and Dunfermline. While at Dunfermline, Hegarty was approached by Inverness CT to be part of the management with former Dundee United colleague Maurice Malpas, although the move never materialised. He was eventually appointed as assistant to Malpas at Motherwell on 25 May 2006, although later replaced by Scott Leitch when Malpas was sacked in June 2007. In March 2008, Hegarty was reported to be one of new Scotland manager George Burley's scouts for the World Cup qualifying group. However, in December 2008 he was appointed as the manager of Livingston after Roberto Landi was sacked. Livingston had severe financial problems, however, and Hegarty left the post a few months later. He has most recently been working as an assistant to George Burley with the Scotland national team until Burley was sacked on November 16. In February 2010 Paul returned 'home' when he took up the position of first team coach at the club he was most successful at as a player, Dundee United. Following the resignation of manager Peter Houston in January 2013, Hegarty was named as the club's caretaker manager, almost exactly a decade after his own dismissal as manager. While he was due to take charge of an SPL match against Motherwell, the match was postponed due to a waterlogged pitch, and Jackie McNamara was named as the club's manager before the next match came around. The new manager soon confirmed that Hegarty would be staying at the club in some capacity, saying 'Heggy will be staying here. He's a tremendous person and a credit to himself the way he's conducted himself the last couple of days.' However, it was announced soon after that Hegarty had left the club.