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About 50 metres to the southeast is a well — Link — that is now generally known as Shear's Well, and which is marked by a water pump and a small associated structure.

That water pump is shown on OS maps from 1914 onwards, but is not marked on the first-edition OS map (surveyed in c.1860). That map does show a well, not at the same place as the later water pump, but about 50 metres to the northwest of it. In 2018, storms brought down a tree, uncovering an old well at or near the location of the well that is marked on the first-edition map. Since the well uncovered in 2018 is near Shear's Well, the two are probably fed by the same source. In early 2019, a new path was created, leading from the edge of the park to the newly-uncovered well.

A manipulable 3D model of the old well was created by Rathmell Archaeology (who investigated the remains), and can be found online at Link (at SketchFab).

In one of his works, "Dumbarton Ancient and Modern" (1893), Donald MacLeod describes the town's Flesh Market, which was built in 1670, and pulled down in 1852. He writes that the slaughter-house of the burgh was in the back part of the premises, and the town's well was in front of them. As he notes, "the town's well ... was supplied by water from St Shear's Well, on the opposite side of the Leven, by a lead pipe laid in 1714 on its bed, the whole works costing £54 sterling."

The course of the lead pipe presumably began near this well, rather than the much later water pump, which is about 50 metres away. Construction of the stone embankment on this side of the Leven probably destroyed any visible surface traces of the pipe's course.

Regarding the laying of that pipe to bring the water across the River Leven, the relevant entries in Dumbarton's Burgh Records are as follows (these entries do not appear in MacLeod's book, but are quoted directly from the burgh records; note that "Kirkton" was an area including the well and the ruined church; a clachan or small settlement beside the church was called Laigh Kirkton or Under Kirkton, in contrast with the higher ground nearby, which is still called Kirktonhill):

27 June 1713: "In consideration of the want of good water in the town, the council resolve to convey St. Shear's Well across the Leven. Sir James Smollett to speak with the Laird of Kirkton thereanent, and to look out for some skilled person to execute the work."

29 May 1714: "The council accept of an offer made by Mr. Cairnaby, Glasgow, to bring St. Shear's Well into the town for £54. The Laird of Kirkton to be spoken to."

9 Oct 1714: "Mr. Cairnaby to be written for, to consult with the council regarding the pipes for bringing in the water."

In dry summer periods, when water was scarce, queues would build up (workers in the town's glassworks were given priority). As noted in "Dumbarton Ancient and Modern", at such times "sometimes the spout at St Shear's well would be resorted to, ... and at other times the Spout Brae, West Bridgend, was visited, and the aqua pura 'tappit' as it flashed from the pipe" (this gives some indication of the source of the well's water).

The lands of Levengrove were originally part of an area named Ferrylands, so called because, before Dumbarton Bridge was built in 1765, the River Leven was crossed by means of a ferry. John Dixon, a Dumbarton merchant, acquired Levengrove in 1805 from Richard Dennistoun of Kelvingrove (in Glasgow).

The Dixons built Levengrove House (demolished c.1880), whose former grounds make up much of what is now the park. In 1885, Levengrove Park, 32 acres in area, was gifted to the town of Dumbarton by Dr Peter Denny and John McMillan (son of local shipbuilder Archibald McMillan), the expense to them being £20,000.

The park contains the ruins of St Serf's Church – Link – anciently the parish church of Cardross. That church was at one time part of a cluster of buildings, a clachan, that is marked as "Little Kirktoun" on the Pont/Blaeu map of the Lennox. The ruined church was later used by the Dixon family as a burial place: see Link (in a Geograph article).