HSE is an indication that appears after the names of pharmaceutical ingredients (APIs and excipients) in PILs (product information leaflets) and SPCs (summaries of product characteristics). Other analogous indications that appear include BP (British Pharmacopoeia), USP (United States Pharmacopoeia) and Ph Eur (European Pharmacopoeia). Here are a couple of examples:

"1. Name of the medicinal product
Cutivate® 0.05% w/w Cream
2. Qualitative and quantitative composition
Fluticasone Propionate (micronised) HSE 0.05% w/w."
https://www.medicines.org.uk/emc/medicine/726#PRODUCTINFO

"1. Name of the medicinal product
SANDO-K®
2. Qualitative and quantitative composition
Effervescent Tablets containing 0.6g potassium chloride Ph.Eur., 0.4g potassium bicarbonate USP"
https://www.medicines.org.uk/emc/medicine/812

These abbreviations indicate the reference standards: they certify that the ingredient conforms to the specifications of the pharmacopoeia indicated. However, HSE is not the name of a pharmacopoeia. It can be the abbreviation of the Irish Health Services Executive or the UK's Health and Safety Executive, but neither of these is relevant here since neither body certifies the specifications of pharmaceutical ingredients.

HSE means "in-house specification"; it’s used when there is no monograph for the ingredient in question in the usual pharmacopoeias, or where such monographs have not been used.

"HSE - In House Specification"
REGULATORY LEXICON
(Common abbreviations in Regulatory Affairs)
http://www.espl-regulatory.com/reglex-feb2016.pdf

"Active substance not described in a pharmacopoeia
For active substances not described in a pharmacopoeia, the in-house specification
should be provided."
http://lenus.ie/hse/bitstream/10147/96980/1/ProductDossier06...

"Analytical methods used in the laboratories are primarily pharmacopoeial, taken from the British Pharmacopoeia or European Pharmacopoeia or from other international pharmacopoeias as appropriate. However, in many cases no suitable official monograph exists, so in-house specifications are developed and validated."
Martin Stephens, ed., Hospital Pharmacy, p. 103
http://202.74.245.22:8080/xmlui/bitstream/handle/123456789/4...

This one is a bit long, but usefully explicit:

"Ingredient.................................................Ref std
Amoxicillin THD erial) (as trihydrate)......Ph Eur/HSE
Clavulanic acid [...]....................................Ph Eur/HSE
Xanthan gum..............................................Ph Eur/NF
Succinic acid..............................................HSE
Colloidal silicon dioxide............................Ph Eur/USP
[...]
Strawberry powder flavour........................HSE
Orange powder flavour..............................HSE
[...]
EXCIPIENTS
Xanthan gum, colloidal silicon dioxide, saccharin sodium, hydroxypropylmethyl cellulose (hypromellose) and silicon dioxide are specified as complying with published Ph Eur monographs. Xanthan gum, colloidal silicon dioxide and hypromellose are additionally specified as complying with corresponding USP/NF monographs. [...] An ‘in house’ specification for succinic acid has been provided, based on the supplier’s own specification. Satisfactory evidence of compliance has been presented. In-house specifications have also been provided for the strawberry, orange and lemon flavouring agents."
http://www.mhra.gov.uk/home/groups/par/documents/websitereso...


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Note added at 11 hrs (2016-05-08 07:03:15 GMT)
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One more for luck:

" 10 mg tablet
Obeticholic acid 10.0 mg* API HSE
Microcrystalline cellulose 176.0 mg* Filler/Binder USP-NF/EP/JP
[...]
API: Active pharmaceutical ingredient
HSE = In house specification
USP-NF = US Pharmacopeia National Formulary
Ph Eur = European Pharmacopeia
JP =Japanese Pharmacopeia"
http://www.google.com/patents/WO2013192097A1?cl=en