Born in Biella, Piedmont region, Beltrame began his youth career with Novara Calcio. He was signed by Juventus F.C. in 2011 in a co-ownership deal, for €750,000, where in the Primavera squad, with whom he graduated the youth academy in June 2013 after helping the club to several youth-team accolades, including the 2013 Coppa Italia Primavera and the 2012 Torneo di Viareggio. During the 2012–13 Serie A season, Beltrame also began to earn a handful of first-team call-ups by head coach, Antonio Conte. Juventus also signed Beltrame outright for an additional fee of €750,000. He made his debut for Juventus on 26 January 2013 against Genoa, coming on as an 82nd-minute substitute for Claudio Marchisio, as the club was searching for a win during a 1–1 draw. Beltrame nearly scored just minutes after his introduction if not for a vital save by Sebastien Frey.
On 2 September 2013, Beltrame was signed by Bari on a one-year loan deal from Juventus. In January 2014, however, half of the registration rights of his contract was swapped with 50% registration rights of Vincenzo Fiorillo of Sampdoria. Under the joint ownership agreement between Juventus and Sampdoria, the player's contractual playing rights would be acquired by Sampdoria and the player would remain on loan with Bari for the remainder of the 2013–14 Serie B season. The co-ownership agreement between Juventus and Sampdora was officially renewed on 18 June 2014.
On 1 July 2014, Beltrame officially joined Sampdoria upon the conclusion of the loan deal, although he it was soon agreed that he would be joining Serie B side, Modena on another season-long loan deal. However, in winter transfer window of 2015, Beltrame returned to Juventus for €1 million in a 4½-year contract, with Jakub Hromada and Atila Varga moved to Sampdoria for €600,000 and €400,000 respectively.
On 27 January 2020, Beltrame signed a permanent deal with Bulgarian club CSKA Sofia, earning a reported €1.5 million per year. He made his official debut on February 15th 2020 in the Eternal Derby against Levski Sofia, starting from the first minute and being substituted 10-minutes before the end. In his second match against Botev Plovdiv on 22 February he scored his first goal for CSKA Sofia securing a 1-0 victory and deservingly being named Man of the Match. He scored his second goal for the club against FC Tsarsko Selo Sofia in a 2-1 defeat.
International career
Beltrame has represented Italy at the U-18, U-19, and U-20 international levels. He has 7 goals in 19 youth international matches, and has been a key component in Italy's U-19 UEFA Euro qualifiers.
