Letica kicked off his career with Hajduk Split in 2015 after arriving to the academy in 2008. He spent the initial years in loan spells.[4] His first loan spell came in February 2015, when he joined Mosor of the third tier along with five other Hajduk players.[5] His second loan spell was to NK Val of the same tier.[6] In August 2016, he was loaned off again, this time to second tier club Rudeš where he made his debut in the Croatian Football Cup qualifiers.[7]
In August 2017, Letica made his debut for Hajduk when he featured in a 1–0 league victory against Slaven Belupo where he kept a clean sheet.[8][9] On 11 March 2018, Letica scored his first professional goal in injury time against Istra 1961 for a 3–2 victory.[10]
Club Brugge
On 15 June 2018, Letica moved abroad and signed a four-year contract with Belgian club Club Brugge.[11]
SPAL (loan)
On 20 August 2019, Letica joined Italian Serie A club SPAL on loan with an option to buy.[12]
Sampdoria (loan)
On 5 October 2020, Letica joined Italian Serie A club Sampdoria on loan with an option to buy.[13]
CFR Cluj
On 11 October 2021, he moved to Romania to sign with defending Liga I champions CFR Cluj.[14]
Hermannstadt
On 12 October 2022, Letica joined Romanian Liga I club Hermannstadt agreeing to a one-year deal, with an option to extend for a further year.[15]