As a poet, Jenna's writing has been published widely in journals of international repute, including Poetry Review, The White Review, The Rialto, The Stinging Fly, and Oxford Poetry. Her debut poetry collection, Fortune Cookie (2017), was awarded the Melita Hume Prize and shortlisted for a Somerset Maugham Award. In 2018, Jenna received an Eric Gregory Award from the Society of Authors. Additionally, she was shortlisted for the inaugral Rebecca Swift Women Poets' Prize, commended in the University of Hertfordshire Single Poem Prize, and placed second in the Newcastle Poetry Prize. A pamphlet, CLAKE / Interview For, was published by Verve Poetry Press in 2018, and a micro-pamphlet of poems I can't promise you anything but whale fall / for you was published by Broken Sleep Books in 2021. Her second full-length poetry collection, Museum of Ice Cream was published by Bloodaxe in 2021, and was featured in The TLS and The Telegraph, and named as one of the best poetry books of 2021 by The Telegraph, The F-Word, and the Poetry Book Society. Jenna additionally reviews poetry for Poetry London, Poetry School, and the Poetry Review.

Her debut novel, Disturbance, was published by Trapeze in the UK and W.W. Norton in the US in 2023, and was shortlisted for the Nota Bene Prize in 2024. 

Her academic monograph, Whiteness, Feminism and the Absurd in Contemporary British and US Poetry was published by Edinburgh University Press in 2025.