Scotland and the Republic of Ireland were drawn together in League B, having last played each other during qualification for Euro 2016. Scotland won 1-0 at home, while the return match in Dublin finished 1-1.
The other teams alongside them in Group B1 are Euro 2020 quarter-finalists Ukraine and Armenia.
Scotland face Ukraine in a World Cup play-off in March, but Clarke said: “Being drawn against Ukraine doesn’t add anything to the play-off match at all.
“The game in March, everyone knows the magnitude of that game and the importance of it. We’ve got good opponents to look forward to in the Nations League but all my thoughts in the coming weeks will be centred on the game against Ukraine and hopefully a follow up against Wales and Austria.”
Group matches will be played in June and September next year, with the four group winners in League A competing in the finals in June 2023.
Clarke added: “When you’re in a draw with teams of the same level you’re going to expect three difficult opponents. That’s what we got. It’s a good draw.
“The games against the Republic of Ireland will always be good for the supporters and hopefully we can make them good on the pitch for both sets of fans.
“Obviously we have Ukraine in the World Cup play-offs. We will know them well by the end of the Nations League, we will have played them three times.
“Armenia is a new one, Scotland haven’t played them before so a first for Scotland and a first for Armenia. They are a relatively new nation and have had a couple of good results. They beat Romania and Iceland, so they are a decent team.
“So, three good opponents and something to look forward to in the summer.
He added: “Stepping up to Group A of the Nations League is a realistic target for us but it’s also a realistic target for all four teams in the group.”
England face a reunion with European champions Italy in next year's Nations League and another grudge match with Germany.
Gareth Southgate's side were also drawn to face Hungary.
Wales, promoted to League A following the 2020-21 Nations League competition, face tough opposition in the shape of Belgium, Holland and Poland.
Northern Ireland, who were relegated to League C in the 2020-21 competition, face 2004 European champions Greece in Group C2. They also face Kosovo and the winner of the playout tie between Cyprus and Estonia, which will be played in March next year.
A decision on whether, and how, the 2022-23 Nations League will slot into qualifying for Euro 2024 will be taken when the regulations for that tournament are fixed next June.
UEFA and FIFA faced criticism over the fact that a two-match stadium ban imposed on the Hungarian federation by the European confederation over homophobic and racist behaviour by the country's fans at all three of their Euro 2020 matches was not applied for the World Cup qualifiers, a FIFA competition.
The UEFA sanction will apply for Hungary's first two Nations League matches.