As a practising Christian, Kotva was regarded as politically suspect and potentially disloyal by the Czechoslovak communist administration; he was permitted to teach only in remote rural regions.
He won critical acclaim for his roles in classical Russian drama, including Gogol's The Government Inspector and The Cherry Orchard by Anton Chekhov.
[3] His film debut in 1966 came with a role as a railway supervisor in Jiří Menzel's Oscar-winning Closely Watched Trains.
He appeared too in the 1966 Czechoslovak New Wave film Hotel pro cizince, by Antonín Máša, playing a vagabond, and in 1968's The Cremator by Juraj Herz.
The majority of his roles, and those for which he is best known in Czech cinema, featured Kotva as a supporting actor, often playing shy, introverted and odd personalities.