May Evening Prayer (Vespers) be celebrated in the presence of the exposed Blessed Sacrament?
Yes. “Part of the liturgy of the hours, especially the principal hours, may be celebrated before the Blessed Sacrament when there is a lengthy period of exposition. This liturgy extends the praise and thanksgiving offered to God in the Eucharistic celebration to the several hours of the day; it directs the prayers of the Church to Christ and through him to the Father in the name of the whole world” (HCW, no. 96).