The former Real Madrid youth player has been on goalscoring form for Atletico Malagueno, Malaga's reserve team, who top Group 9 of the Spanish third tier.
Kilmarnock's Greg Taylor and Celtic's Jamie McCart, on loan at Inverness Caledonian Thistle, are the new additions in defence.
St Mirren's Stephen Mallan is among the new crop of midfielders.
Motherwell's Dom Thomas and Celtic's Joe Thomson are rewarded for their loan spells with Queen of the South in the Scottish Championship by being included in the squad for the friendly at Paisley 2021 Stadium on 28 March.
St Mirren's stadium will be a familiar venue for Celtic's Paul McMullan, who had a spell there on loan before his present stint with Dunfermline Athletic, and the Buddies' Lewis Morgan, who are the new forwards along with Harper in Scot Gemmill's squad.
Wolves' Jack Ruddy, who began his career with Real Murcia, is one of two uncapped goalkeepers.
The other is Devlin Mackay, who is on loan to Berwick Rangers in Scotland's League Two from Kilmarnock.
Goalkeepers: Ryan Fulton (Liverpool, loan to Chesterfield), Devlin Mackay (Kilmarnock, loan to Berwick Rangers), Jack Ruddy (Wolverhampton Wanderers)
Defenders: Alex Iacovitti (Nottingham Forest), Zak Jules (Reading, loan to Motherwell), Jamie McCart (Celtic, loan to Inverness CT), Jordan McGhee (Hearts, loan to Middlesbrough), Liam Smith (Heart of Midlothian), Greg Taylor (Kilmarnock)
Midfielders: Chris Cadden (Motherwell), Liam Henderson (Celtic), Stephen Mallan (St Mirren), James Jones (Crewe Alexandra), Dominic Thomas (Motherwell, loan Queen of the South), Ruben Sammut (Chelsea), Joe Thomson (Celtic, loan to Queen of the South)
Forwards: Ryan Hardie (Rangers, loan to Raith Rovers), Jack Harper (Malaga CF), Oliver McBurnie (Swansea City), Paul McMullan (Celtic, loan to Dunfermline Athletic), Lewis Morgan (St Mirren), Craig Wighton (Dundee)
Malaga forward Jack Harper is among 10 uncapped players named in the Scotland Under-21 squad to face Estonia.