$ContextPath//FullForm

$Context

PrependTo[$ContextPath,"PBWAlgebra`gl`"]

"PBWAlgebra`"~~__ //FullForm

Select[$ContextPath, Not@*StringMatchQ["PBWAlgebra`"~~__]]

SetAlgebra[alg_String]:=Module[{cntxt},
cntxt="PBWAlgebra`"<>alg<>"`";
$ContextPath=Prepend[
Select[$ContextPath, Not@*StringMatchQ["PBWAlgebra`"~~__]],
cntxt
];
ToExpression[cntxt<>#]&/@{"m","Δ"}
]

SetAlgebra["gl"]

Context[m]

m=7

SetAlgebra["sl"]

Context[m]

m

gl`m

PBWAlgebra`gl`m

m=3

m

SetAlgebra["gl"]

$ContextPath

Context[m]

Contexts[]