[4] Alexander left Rangers in 2013 after a dispute over wages, having won the Scottish Third Division title at the first attempt, to join Premier League side Crystal Palace.

[5] Alexander started his career with local youth side Edina Hibs in Niddrie, Edinburgh and attracted interest from Arbroath, agreeing scholarship terms with the club.

[10] On 28 May 2001, he joined Football League Second Division side Cardiff City for a nominal fee of £130,000,[10][11][12] with chairman Sam Hammam stating his belief that Alexander had the potential to play at international level in the future.

[17] The club went on to achieve promotion by winning the 2003 Football League Second Division play-off final against Queens Park Rangers following Andy Campbell's extra-time winner.

[18] During his time at Cardiff, Alexander became a fan favourite, despite nearly leaving the club midway through his six-year spell after falling behind Martyn Margetson and Tony Warner following their promotion to the First Division under manager Lennie Lawrence.

[26] On his arrival at Portman Road, Alexander immediately became first choice goalkeeper at the club and made his debut in a 4–1 win against Sheffield Wednesday on 11 August 2007 in the opening match of the 2007–08 season.

[29] His final appearance for the club came on 29 January 2008 in a 0–0 draw with Plymouth Argyle, during which he saved a penalty from Steven MacLean to keep a clean sheet.

[31] Alexander made his debut for Rangers on 3 February 2008, coming on as a substitute after Allan McGregor had been sent off in a Scottish Cup tie at Hibernian.

With McGregor injured, Alexander remained in place for the 2008 UEFA Cup Final against Zenit Saint Petersburg but was unable to prevent a 2–0 defeat.

The following season, McGregor returned to first choice goalkeeper despite Rangers manager Walter Smith stating that the decision was "unfair" on Alexander following his performances.

[45][46] Allan McGregor refused to transfer his contract,[47] which meant that Alexander became first choice 'keeper at Rangers as they embarked on a campaign in the fourth tier of the Scottish football league system.

[51] After the court case, Alexander claimed that he had received "sickening abuse" from Rangers fans when he returned to the club as a Hearts player.

He eventually signed for newly promoted Premier League side Crystal Palace on an initial one-year deal on 14 August 2013,[53] as understudy to Julián Speroni.

[45] He made his debut in a 2–1 League Cup defeat against Bristol City on 27 August 2013 that was his only appearance for the club during the 2013–14 season and he was released by Palace on 1 July 2014 following the expiration of his contract.

[54][55] In June 2014, Alexander signed for Heart of Midlothian, the club he supported as a boy,[7] following their relegation to the Scottish Championship at the end of the 2013–14 season in a dual role as a player-coach, eventually completing the transfer on 1 July following the expiration of his contract at Crystal Palace.

[57] He was replaced by substitute Scott Gallacher and traveled to a local hospital where it was confirmed that Alexander had suffered a broken cheekbone and was subsequently kept out of action for a month,[7] making his return in a 0–0 draw with Dumbarton on 13 September.

[61][62] Neilson later revealed that he took the decision to release Alexander as he felt that his highly rated understudy Jack Hamilton was ready to take over as the club's first choice goalkeeper.

"[66] In March 2017, Aberdeen manager Derek McInnes confirmed that Alexander would not be offered an extension to his contract and he left the club at the end of the season without making a first-team appearance.

[69] He joined the club "to play matches, to see out my career" and made his second debut in a 1–1 draw with Partick Thistle in the Scottish League Cup.

He was called up a second time in August 2002 for a UEFA Euro 2004 qualifying group match against Faroe Islands after Neil Sullivan was forced to withdraw due to injury.

[78] In March 2022 Alexander joined John Hughes's Dunfermline Athletic backroom team as goalkeeping coach following the departure of Owain Fon Williams.

Due to injuries, Dunfermline registered Alexander as a player for the remainder of the season and he immediately went in to the match day squad versus Arbroath as a substitute.