The incident happened at Fayre Oaks Drive off Kings Acre Road, where three common lime trees, initially appearing healthy, were affected by Storm Darragh.
One of the trees revealed extensive decay at its base after collapsing during the storm.
Now, the resident wants to re-pollard the remaining two trees to prevent further potential failures.
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The application for this work, submitted by Mr J Woodall, was received and validated by Herefordshire Council on January 13.
The trees (highlighted in blue) are in Fayre Oaks Drive (Image: www.herefordshire.gov.uk) The trees are in an area covered by a Tree Preservation Order (TPO), which necessitates official consent for any work.
The application said the work will be carried out by Trilloes Tree Care Ltd.
The consultation period for the application has already begun, with public comments accepted until February 14.
The assessment will be conducted by case officer Andrew Cunningham.
The target date for determining the application is March 10.
The Hereford City Council and local councillors Robert Williams and Dave Boulter have also been consulted regarding the proposal.