The Hoops earned their place in UEFA's elite club competition after winning the 2022 League of Ireland, while Breidablik were champions in their respective league last year.
Match preview
Shamrock Rovers are back in Champions League action following their title-winning campaign of 2022, with the Hoops finishing 13 points clear of second-placed Derry City in the final standings.
Stephen Bradley's men have won the last three league crowns in Ireland, but success for the club on the continental stage is a lot more limited.
The Hoops made their debut in the Europa Conference League group stage last season, the club's first appearance past the qualifying rounds of a European competition since they made a 2011-12 Europa League group which included Tottenham Hotspur and Rubin Kazan.
A section made up of Gent, Molde and Djurgarden IF proved too challenging for Bradley's side, with Shamrock only managing to collect two points in six matches.
Rovers are heading towards a fourth-straight title in Ireland this year, currently sitting four points ahead of second-placed St Patrick's Athletic in the League of Ireland standings.
Breidablik have not been as consistent with earning league titles as their Irish opponents on Tuesday night, but the Icelandic outfit also won their domestic league in 2022 to secure a place in the Champions League qualifying rounds.
Blikar finished 10 points clear of KA Akureyri last year, winning their first Besta Deildin crown since 2010, with that success over a decade ago being the club's only other league title.
Oskar Thorvaldsson's men had to win two matches in the preliminary round of qualifying to book a clash with Shamrock Rovers - a task which Breidablik made easy work of, thrashing Tre Penne Galazzano 7-1 before beating Buducnost Podgorica 5-0.
The furthest the Icelandic champions have ever been in European competition was the third qualifying round of the Europa League in 2013, although a penalty shootout loss against Latvian side FK Jelgava ended their continental journey on that occasion.
Shamrock Rovers form (all competitions):
W
W
D
W
L
D
Breidablik Champions League form:
W
W
Breidablik form (all competitions):
Team News
Shamrock have a packed-out medical room ahead of a crucial Champions League meeting on Tuesday night, with Lee Grace and Jack Byrne both doubts due to muscle injuries.
Full-back duo Neil Farrugia and Trevor Clarke will definitely miss the match, with the defenders expected to be sidelined until late July and September respectively.
Breidablik are expected to name a similar XI to the one which breezed past Buducnost Podgorica in Kopavogur on June 30, with Hoskuldur Gunnlaugsson looking to add to his three Champions League goals so far this season.
Stefan Sigurdarson has started his 2023 league campaign in blistering fashion, scoring 10 goals in just nine Besta Deildin starts, and the 22-year-old should be handed another start in Dublin on Tuesday.
Shamrock Rovers possible starting lineup:
Pohls; Lopes, Kavanagh, Cleary, Hoare; Poom, Nugent, Watts; Gaffney, Kenny, Burke
Breidablik possible starting lineup:
Einarsson; Gunnlaugsson; Muminovic, Adalsteinsson, Yeoman; Steindorsson, Sigurjonsson, Margeirsson; Einarsson, Eyjolfsson; Sigurdarson
We say: Shamrock Rovers 1-0 Breidablik
Shamrock are experiencing a mini-wobble in the League of Ireland but will be confident of putting recent struggles behind them with a victory over Breidablik in the first leg.
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