Born in Lambeth, Vose came through the youth system at Fulham, and during his time there, had trials at Manchester United and Arsenal. He later joined West Ham United, making his debut for their reserves at the age of 16 before signing his first professional contract on his 17th birthday. He joined Braintree Town in the Conference Premieron loan for one month in October 2011. Vose was released by West Ham in December 2012. Later that month, he signed for Tooting & Mitcham United, scoring one goal in four appearances. In January 2013, Vose went on trial with Stoke City, before signing a one-year deal at Barnet in February 2013. He made two appearances for Barnet in Football League Two; his debut as a 90th-minute substitute for Jon Nurse in a 2–0 win over Fleetwood Town on 19 March 2013, and his second when he came on as substitute on the final day of the season against Northampton Town. He left Barnet by mutual consent in August 2013. On 1 November 2013, Vose signed for Colchester United on a monthly contract after impressing on trial with the club. He made his debut for the U's as a substitute for Craig Eastmond in the club's FA Cup first round defeat to Sheffield United on 9 November 2013. After making his first league appearance as a substitute for Ryan Dickson during a 1–1 draw with Preston North End on 23 November, Vose made his first start for Colchester on 26 November in a 3–1 win against Milton Keynes Dons three days later, before being substituted for eventual goalscorer Macauley Bonne on 68 minutes. In January 2014, Vose signed a contract with Colchester until the end of the season. He then extended his stay with the club by signing a two-year contract in May 2014. However, after making only a handful of appearances under new Colchester manager Tony Humes, Vose agreed to cancel his contract with the club by mutual consent on 2 December 2014 in order to seek first team football elsewhere.
In May 2015, he signed for National League club Wrexham on a one-year deal. He made his debut in the first game of the 2015–16 season for Wrexham in the 3–1 away defeat to Bromley.
Scunthorpe United
On 1 February 2016, Vose signed a -year contract with League One side Scunthorpe United for an undisclosed fee. Prior to him signing on transfer deadline day, a bid from rival National League side Grimsby Town was allegedly accepted, but apparently Vose wasn't willing to make the move, initially wanting to play out the season at Wrexham. However, later on, a statement by the Chief Executive at Wrexham denied Vose's claims that the Dragons had accepted a Mariners' bid: "We had an offer and they were being considered, but nothing had been accepted formally," adding that the decision to let him leave was purely for footballing reasons, earning a move to a club two divisions higher in the pyramid. Vose made his debut for the club on 5 March 2016, coming on as a substitute on 85 minutes in the 0–0 draw at home to Gillingham. His only other appearance for the 2015–16 season was on 2 April 2016 in the 1–0 away defeat to Bradford City, coming off the bench in the 81st minute. Vose continued to struggle to break into the first-team and signed a season-long loan with newly promoted League Two side Grimsby Town, which would keep him there until the end of the 2016–17 season. Scunthorpe released him at the end of the season.
Whitehawk
After being without a club for the start of the 2017–2018 season, Vose signed for National League South Whitehawk in October 2017.
Bromley
Following his departure from Whitehawk, Vose trained with Bromley and eventually signed for the club on 10 November, making his debut the following day and earning an injury time assist in a 1–0 win away to Guiseley.
