This arrangement focuses entirely on left-hand technique to perform the famous hymn melody. It is distinctive for challenging the performer to extract a melodic line and accompaniment from a single hand.
The primary challenge is balancing the melodic voicing while simultaneously managing the accompaniment figurations with a single hand.
Comparable difficulty and character — good candidates for what to learn next.
'Hark the Herald' Arranged for Left Hand is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 6.
You should be comfortable at Henle level 4 — meaning you can already play level 3–4 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of 'Hark the Herald' Arranged for Left Hand lasts about 4 minutes.
'Hark the Herald' Arranged for Left Hand is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 'Elfentanz' Arranged as a Left Hand Study by George Arthur Meyer, Blaubart by Karl Michael Ziehrer, The Entertainer by Scott Joplin — see the full similar-pieces list on this page.